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Math Help - Number Pattern

  1. #1
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    Number Pattern

    Consider the pattern.

    5^3=125

    5^4=625

    5^5=3125

    5^6=15625

    Use this pattern to write out the last 3 digits of  5^{15} .

    How can I work this out?
    Last edited by JadeKiara; September 19th 2009 at 11:47 PM. Reason: fix some LaTeX
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by JadeKiara View Post
    Consider the pattern.

    5^3=125

    5^4=625

    5^5=3125

    5^6=15625

    Use this pattern to write out the last digits of  5^{15} .

    How can I work this out?
    1. You do not specify how many digits constitute "the last" digits of 5^{15}.

    2. A suitable hypothesis might be that the last two digits of 5^n for n\ge 2 are 25.

    3. Suppose this true for k that is 5^k=100 \times M+25 for some integer M, now 5^{k+1}= ...

    NOw can you take it from there?

    CB
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  3. #3
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    Sorry, it was the last three digits. This was easier than I thought! How silly of me!!

    Seeing as odd indices always result in ending digits of 125, and even indices result in 625, the answer to this problem would be 125. Am I right?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by JadeKiara View Post
    Sorry, it was the last three digits. This was easier than I thought! How silly of me!!

    Seeing as odd indices always result in ending digits of 125, and even indices result in 625, the answer to this problem would be 125. Am I right?
    yes

    CB
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